Second-order Response Theory Research Articles

Quadratic optical responses in a chiral magnet

Chiral magnets, which break both spatial inversion and time reversal symmetries, carry a potential for quadratic optical responses. Despite the possibility of enhanced and controlled responses through the magnetic degree of freedom, the systematic understanding remains yet to be developed. We here study nonlinear optical responses in a prototypical chiral magnetic state with a one-dimensional conical order by using the second-order response theory. We show that the photovoltaic effect and the second harmonic generation are induced by asymmetric modulation of the electronic band structure under the conical magnetic order, and the coefficients, including the sign, change drastically depending on the frequency of incident lights, the external magnetic field, and the strength of spin-charge coupling. We find that both effects can be enormously large compared to those in the conventional nonmagnetic materials. Our results would pave the way for next-generation optical electronic devices, such as unconventional solar cells and optical sensors, based on chiral magnets.

Coarse-grained second-order response theory

While linear response theory, manifested by the fluctuation dissipation theorem, can be applied at any level of coarse graining, nonlinear response theory is fundamentally of microscopic nature. For perturbations of equilibrium systems, we develop an exact theoretical framework for analyzing the nonlinear (second order) response of coarse grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse grained path weights. The time symmetric part of these weights depends on the paths and perturbation protocol in a complex manner; in addition, the absence of Markovianity prevents slicing of the coarse-grained path integral. We show that these difficulties can be overcome and the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme where measuring linear responses of coarse-grained variables suffices to determine their second order response. We illustrate the validity of the formalism with an exactly solvable four-state model and the near-critical Ising model.

Second-order response theory of radio-frequency spectroscopy for cold atoms

We present a theoretical description of the radio-frequency (rf) spectroscopy of fermionic atomic gases, based on the second-order response theory at finite temperature. This approach takes into account the energy resolution due to the envelope of the rf pulse. For a noninteracting final state, the momentum- and energy-resolved rf intensity depends on the fermion spectral function and pulse envelope. The contributions due to interactions in the final state can be classified by means of diagrams. Using this formalism, as well as the local density approximation in two and three dimensions, we study the interplay of inhomogeneities and Hartree energy in forming the line shape of the rf signal. We show that the effects of inhomogeneities can be minimized by taking advantage of interactions in the final state, and we discuss the most relevant final-state effects at low temperature and density, in particular the effect of a finite lifetime.

Spin-orbit coupling in molecular Auger spectra: propensity rules tested for water

Electronic spectra of dicationic molecules comprise a high density of singlet and triplet states. By virtue of simple propensity rules only the singlet states are selected by core-valence (CVV) Auger spectroscopy. The authors use second-order response theory to explore the role of spin-orbit interaction in the manifold of low-lying dicationic states and its implications on the intensity analysis of the Auger spectrum of water.

Quadratic response of a chemical reaction to external oscillations

We develop a second-order response theory to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor. We apply the theory to the quadratic Schlögl model, a single-variable nonlinear reaction. In the presence of oscillating reactant or product concentrations or oscillating rate coefficients, the average intermediate concentration, the fluxes, and the dissipation are each a Lorentzian function of frequency with midpoint at the inverse relaxation time of the system. Thus even very short relaxation times can be determined by measuring average rates as a function of frequency of the perturbation. The amplitude of the Lorentzian depends on the chemical mechanism of the reaction and is proportional to the square of the amplitude of the applied perturbation. We also show that energy from the perturbation can be used to drive the reaction in a direction opposite of that predicted by the Gibb’s free energy difference of reactants and products, even under circumstances where the overall affinity is independent of the perturbation.